All categories

3 years ago

The formula for area of a circle can be found by using a parallelogram explain the way to derive the formula

Mathematics

2 answers:

Leto [7]3 years ago

7 0

Answer:

The circle can be cut into slices, separated, and fit together to form a parallelogram that has the same area. The height of the parallelogram is the radius and the base is half the circumference, which is

expeople1 [14]3 years ago

6 0

Step-by-step explanation :

The base and height of the parallelogram describe the parts of the circle.
Let us consider B as base and H as the height of the parallelogram. Base b is equal to half of the circumference of the circle.
To determine the area of the circle, substitute r for h and πr for b in the area formula by considering r as the radius of the circle.
Therefore, the formula to find the area of a circle is πr² square units.

You might be interested in

What is the common ratio of the geometric sequence below? –2, 4, –8, 16, –32, ...

SOVA2 [1]

Answer:

The common ratio of the geometric sequence is:

$r=-2$

Step-by-step explanation:

A geometric sequence has a constant ratio 'r' and is defined by

$a_n=a_1\cdot r^{n-1}$

where

aₙ is the nth term

a₁ is the first term

r is the common ratio

Given the sequence

$-2,\:4,-8,\:16,\:-32,\:...$

Compute the ratios of all the adjacent terms: $r=\frac{a_n+1}{a_n}$

$\frac{4}{-2}=-2,\:\quad \frac{-8}{4}=-2,\:\quad \frac{16}{-8}=-2,\:\quad \frac{-32}{16}=-2$

The ratio of all the adjacent terms is the same and equal to

$r=-2$

Therefore, the common ratio of the geometric sequence is:

$r=-2$

5 0

3 years ago

Please help! 40 points! 2 answer choice questions.<br> will give: Brainliest, Rattings, Thanks, etc.

ivann1987 [24]

Answer:

7. Positive association

8. No association

Step-by-step explanation:

7. In this scatterplot, the points form a rough line that goes higher as the x values increase. In other words, it's tilting up, and its slope is positive. This signifies a positive association or correlation.

8. In this scatterplot, there seems to be no particular pattern; the points are random. Notice how there is no rough line or shape formed by these points. Since there is no relationship between "Salary" and "Height," there is no association or correlation.

7 0

3 years ago

The owner of a ski resort estimates that a new 4-person ski lift will cost $5,500,000. The owner begins making payments on March

disa [49]

Amount must the owner make to have the cost of the ski lift in 5 years is $6,711,045.22.

<h3>What is compound interest?</h3>

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.

A = P(1 + r/n) $^{nt}$

P =5,500,000

r =4%= 0.004

n =4

t= 5 years.

Now,

A = P(1 + r/n) $^{nt}$

A = 5,500,000.00(1 + 0.04/4) $^{(4)(5)}$

A = 5,500,000.00(1 + 0.01) $^{20}$

A = $6,711,045.22

Hence, The total amount accrued is $6,711,045.22.

Learn more about compound interest here:

brainly.com/question/14295570

#SPJ1

7 0

2 years ago

A tobacco company claims that the amount of nicotene in its cigarettes is a random variable with mean 2.2 and standard deviation

Aleksandr-060686 [28]

Answer:

0% probability that the sample mean would have been as high or higher than 3.1 if the company’s claims were true.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 2.2, \sigma = 0.3, n = 100, s = \frac{0.3}{\sqrt{100}} = 0.03$

What is the approximate probability that the sample mean would have been as high or higher than 3.1 if the company’s claims were true?

This is 1 subtracted by the pvalue of Z when X = 3.1. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{3.1 - 2.2}{0.03}$

$Z = 30$

$Z = 30$ has a pvalue of 1.

1 - 1 = 0

0% probability that the sample mean would have been as high or higher than 3.1 if the company’s claims were true.

4 0

4 years ago

Which transformations are needed to change the parent cosine function to<br> y = 0.35cos(8(x-pi/4))

Levart [38]

Here's a list of the changes and their effect:

$\begin{array}{c|c|c}\text{From}&\text{To}&\text{Effect}\\\cos(x)&\cos\left(x-\frac{\pi}{4}\right)&\text{Horizontal shift}\\\cos\left(x-\frac{\pi}{4}\right)&\cos\left(8\left(x-\frac{\pi}{4}\right)\right)&\text{Horizontal compression}\\\cos\left(8\left(x-\frac{\pi}{4}\right)\right)&0.35\cos\left(8\left(x-\frac{\pi}{4}\right)\right)&\text{Vertical compression}\end{array}$

So, the function is shifted $\frac{\pi}{4}$ units to the right, then it is compressed by a factor 8 horizontally, and a factor 0.35 vertically.

8 0

3 years ago

Read 2 more answers